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2 years ago

Use the point-slope form from the previous question and fill-in the following table of values.

Mathematics

1 answer:

matrenka [14]2 years ago

8 0

Answer:

Step-by-step explanation:

Slope of line through (0,-1) and (1,2) = (-1 - 2)/(0 - 1) = 3

Point-slope equation for line of slope 3 that passes through (0,-1):

y+1 = 3(x-0)

When x = 2:

y+1 = 3(2-0)

y = 3·2 - 1 = 5

When x = 3:

y+1 = 3(3-0)

y = 3·3-1 = 8

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Consider the system of differential equations dxdt=−4ydydt=−4x. Convert this system to a second order differential equation in y

koban [17]

$\dfrac{\mathrm dy}{\mathrm dt}=-4x\implies x=-\dfrac14\dfrac{\mathrm dy}{\mathrm dt}\implies\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac14\dfrac{\mathrm d^2y}{\mathrm dt^2}$

Substituting this into the other ODE gives

$-\dfrac14\dfrac{\mathrm d^2y}{\mathrm dt^2}=-4y\implies y''-16y=0$

Since $x(t)=-\dfrac14y'(t)$ , it follows that $x(0)=-\dfrac14y'(0)=4\implies y'(0)=-16$ . The ODE in $y$ has characteristic equation

$r^2-16=0$

with roots $r=\pm4$ , admitting the characteristic solution

$y_c=C_1e^{4t}+C_2e^{-4t}$

From the initial conditions we get

$y(0)=5\implies 5=C_1+C_2$

$y'(0)=16\implies-16=4C_1-4C_2$

$\implies C_1=\dfrac12,C_2=\dfrac92$

So we have

$\boxed{y(t)=\dfrac12e^{4t}+\dfrac92e^{-4t}}$

Take the derivative and multiply it by -1/4 to get the solution for $x(t)$ :

$-\dfrac14y'(t)=\boxed{x(t)=-\dfrac12e^{4t}+\dfrac92e^{-4t}}$

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2 years ago

What is the value of log subscript 4 baseline 16? 1 2 4 8

dimulka [17.4K]

$~\log_4 16 \\\\= \log_4 4^2\\\\=2 \log_ 4 4~~~~~~~~~~~~~~~~~~~~~~~~;[\log_b m^n = n \log_b m]\\\\=2 \cdot 1~~~~~~~~~~~~~~~~~~~~~~~~~~~~;[ \log_b b =1]\\\\=2$

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1 year ago

What is the quotient of 5/18 ÷ 2/6 ?

Lunna [17]

I know the answer. It would be 5/6.

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2 years ago

GIVING 20 POINTS PLS HELP!!!

ser-zykov [4K]

Answer:

The answer is C. -336

Step-by-step explanation:

All you have to do is 25 - 39 = -14 x 24 = -336

Hope this helps :)

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2 years ago

Keith ate 2/6 of candy bar. If there were 6 pieces total, what fraction of the candy bar is left?

IgorC [24]

If there were 6 pieces and Keith ate 2 of the pieces, then there would be 4 pieces left.
$\frac{4}{6}$
and when you reduce it it would be
$\frac{2}{3}$

5 0

2 years ago

Read 2 more answers